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Floquet perturbation theory for periodically driven weakly interacting fermions
Physical Review B ( IF 3.2 ) Pub Date : 2020-12-04 , DOI: 10.1103/physrevb.102.235114
Roopayan Ghosh , Bhaskar Mukherjee , K. Sengupta

We compute the Floquet Hamiltonian HF for weakly interacting fermions subjected to a continuous periodic drive using a Floquet perturbation theory (FPT) with the interaction amplitude being the perturbation parameter. This allows us to address the dynamics of the system at intermediate drive frequencies ωDV0J0, where J0 is the amplitude of the kinetic term, ωD is the drive frequency, and V0 is the typical interaction strength between the fermions. We compute, for random initial states, the fidelity F between wave functions after a drive cycle obtained using HF and that obtained using exact diagonalization (ED). We find that FPT yields a substantially larger value of F compared to its Magnus counterpart for V0ωD and V0J0. We use the HF obtained to study the nature of the steady state of an weakly interacting fermion chain; we find a wide range of ωD which leads to subthermal or superthermal steady states for finite chains. The driven fermionic chain displays perfect dynamical localization for V0=0; we address the fate of this dynamical localization in the steady state of a finite interacting chain and show that there is a crossover between localized and delocalized steady states. We discuss the implication of our results for thermodynamically large chains and chart out experiments which can test our theory.

中文翻译:

周期性驱动的弱相互作用费米子的浮球摄动理论

我们计算Floquet哈密顿量 HF使用Floquet摄动理论(FPT),以连续振幅为驱动力的弱相互作用的费米子,其相互作用振幅为摄动参数。这使我们能够解决中等驱动频率下的系统动态问题ωdV0Ĵ0,在哪里 Ĵ0 是动力学项的振幅, ωd 是驱动频率,并且 V0是费米子之间典型的相互作用强度。对于随机初始状态,我们计算保真度F 使用以下方法获得的驱动周期后的波动函数之间 HF以及使用精确对角化(ED)获得的结果。我们发现FPT产生的值要大得多F 与马格努斯同行相比 V0ωdV0Ĵ0。我们使用HF获得以研究弱相互作用的费米子链的稳态性质;我们发现各种各样的ωd这会导致有限链的亚热或超热稳态。驱动的铁离子链显示出完美的动力学定位V0=0; 我们解决了有限相互作用链的稳态中这种动态局部化的命运,并表明局部化和离域化稳态之间存在交叉。我们讨论了我们的结果对热力学大链的影响,并提出了可以验证我们理论的实验。
更新日期:2020-12-04
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